Finite Group Databasebeta

← #28513145

Subgroups — #28513145

Order 15104.

2266 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273708C211yesmaximal, characteristic
2C2×#16837290C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×Dic59C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Dic59C211yesmaximal, characteristic, complemented
5#21422362C211yesmaximal, characteristic, complemented
6#21422343C211yesmaximal, characteristic, complemented
7#21422339C211yesmaximal, characteristic, complemented
8#21422337C211yesmaximal, characteristic
9#21422333C211yesmaximal, characteristic, complemented
10#21422327C211yesmaximal, characteristic, complemented
11#21422327C211yesmaximal, characteristic, complemented
12Dic59⋊#95C211yesmaximal, characteristic, complemented
13#21422319C211yesmaximal, characteristic, complemented
14#21422318C211yesmaximal, characteristic, complemented
15C2×C59×#386C211yesmaximal, characteristic
16C24×Dic59C2211yescharacteristic
17C2×#14273708—24no—
18C2×#14273708—24no—
19C2×#14273708C418yescomplemented
20C22×Dic59⋊C4C2211yescharacteristic
21C22×Dic59⋊C4C2211yescharacteristic
22C22×Dic59⋊C4C2211yescharacteristic
23C22×C22⋊Dic59C2211yescharacteristic
24C22×C22⋊Dic59C2211yescharacteristic
25C22×C22⋊Dic59C2211yescharacteristic
26C22×C22⋊Dic59C2211yescharacteristic
27C22×C22⋊Dic59C2211yescharacteristic
28C22×C22⋊Dic59C2211yescharacteristic
29C22×C22⋊Dic59C2211yescharacteristic
30C22×C4×Dic59C2211yescharacteristic
31C22×C4×Dic59C2211yescharacteristic
32C22×C4×Dic59C2211yescharacteristic
33#16837290—24no—
34C22⋊C4×Dic59—24no—
35C4×C22⋊Dic59—24no—
36C2×C59⋊#95C2211yescharacteristic
37C2×C59⋊#95C2211yescharacteristic
38C2×C59⋊#95C2211yescharacteristic
39C2×C59⋊#95C2211yescharacteristic
40C2×C59⋊#95C2211yescharacteristic
41C2×C59⋊#95C2211yescharacteristic
42C2×C59⋊#95C2211yescharacteristic
43C2×C59⋊#95C2211yescharacteristic
44C2×C59⋊#95C2211yescharacteristic
45C2×C59⋊#95C2211yescharacteristic
46C2×C59⋊#95C2211yescharacteristic
47C2×C59⋊#95C2211yescharacteristic
48C2×C59⋊#95C2211yescharacteristic
49C2×C59⋊#95C2211yescharacteristic
50C23×D4×C59C2211yescharacteristic
51C24×C4×C59C2211yescharacteristic
52C22×C22⋊C4×C59C2211yescharacteristic
53C22×C22⋊C4×C59C2211yescharacteristic
54C22×C22⋊C4×C59C2211yescharacteristic
55C59×#386—24no—
56C2×#95×C59C2211yescharacteristic
57C2×#95×C59C2211yescharacteristic
58C23×Dic59—22no—
59C23×Dic59—22no—
60C23×Dic59—22no—
61C23×Dic59—22no—
62C23×Dic59—41no—
63C23×Dic59—41no—
64C23×Dic59C2×C414yescomplemented
65C23×Dic59C2311yescharacteristic
66C23×Dic59C2311yescharacteristic
67C23×Dic59C2311yescharacteristic
68C23×Dic59C2311yescharacteristic
69C23×Dic59C2311yescharacteristic
70C23×Dic59C2311yescharacteristic
71C23×Dic59C2311yescharacteristic
72C23×Dic59C2311yescharacteristic
73#14273708—232no—
74C2×Dic59⋊C4—22no—
75C2×Dic59⋊C4—22no—
76C2×Dic59⋊C4—22no—
77C2×Dic59⋊C4—22no—
78C2×Dic59⋊C4—22no—
79C2×Dic59⋊C4—22no—
80C2×Dic59⋊C4—41no—
81C2×Dic59⋊C4C2×C414yescomplemented
82C2×Dic59⋊C4C2×C414yescomplemented
83C2×C22⋊Dic59—22no—
84C2×C22⋊Dic59—22no—
85C2×C22⋊Dic59—22no—
86C2×C22⋊Dic59—22no—
87C2×C22⋊Dic59—22no—
88C2×C22⋊Dic59—22no—
89C2×C22⋊Dic59—22no—
90C2×C22⋊Dic59—22no—
91C2×C22⋊Dic59—22no—
92C2×C22⋊Dic59—22no—
93C2×C22⋊Dic59—22no—
94C2×C22⋊Dic59—22no—
95C2×C22⋊Dic59—22no—
96C2×C22⋊Dic59—22no—
97C2×C22⋊Dic59—41no—
98C2×C22⋊Dic59—41no—
99C2×C22⋊Dic59C2×C414yes—
100C2×C22⋊Dic59C2×C414yes—
101C2×C22⋊Dic59C2×C414yescomplemented
102C2×C22⋊Dic59D414yes—
103C2×C22⋊Dic59D414yes—
104C2×C4×Dic59—22no—
105C2×C4×Dic59—22no—
106C2×C4×Dic59—22no—
107C2×C4×Dic59—22no—
108C2×C4×Dic59—22no—
109C2×C4×Dic59—22no—
110C2×C4×Dic59—41no—
111C2×C4×Dic59—41no—
112C2×C4×Dic59—41no—
113C59⋊#95—22no—
114C59⋊#95—22no—
115C59⋊#95—22no—
116C59⋊#95—22no—
117C59⋊#95—22no—
118C59⋊#95—22no—
119C59⋊#95—22no—
120C59⋊#95—22no—
121C59⋊#95—22no—
122C59⋊#95—22no—
123C59⋊#95—41no—
124C59⋊#95—41no—
125C59⋊#95—41no—
126C59⋊#95—41no—
127C25×C59C2311yescharacteristic
128C25×C59C2311yescharacteristic
129C22×D4×C59—22no—
130C22×D4×C59—22no—
131C22×D4×C59—22no—
132C22×D4×C59—22no—
133C22×D4×C59—41no—
134C22×D4×C59—41no—
135C22×D4×C59C2×C414yes—
136C23×C4×C59—22no—
137C23×C4×C59—22no—
138C23×C4×C59—22no—
139C23×C4×C59—22no—
140C23×C4×C59—22no—
141C23×C4×C59—41no—
142C23×C4×C59—41no—
143C23×C4×C59C2311yescharacteristic
144C23×C4×C59C2311yescharacteristic
145C23×C4×C59C2311yescharacteristic
146C23×C4×C59C2311yescharacteristic
147C23×C4×C59C2311yescharacteristic
148C2×C22⋊C4×C59—22no—
149C2×C22⋊C4×C59—22no—
150C2×C22⋊C4×C59—22no—
151C2×C22⋊C4×C59—22no—
152C2×C22⋊C4×C59—22no—
153C2×C22⋊C4×C59—22no—
154C2×C22⋊C4×C59—41no—
155C2×C22⋊C4×C59—41no—
156C2×C22⋊C4×C59D414yes—
157#95×C59—22no—
158#95×C59—22no—
159C24×C59—21no—
160C24×C59—21no—
161C24×C59—21no—
162C24×C59—21no—
163C24×C59—21no—
164C24×C59—21no—
165C24×C59—21no—
166C24×C59—21no—
167C24×C59—21no—
168C24×C59—21no—
169C24×C59—21no—
170C24×C59—21no—
171C24×C59—21no—
172C24×C59—21no—
173C24×C59—21no—
174C24×C59—21no—
175C24×C59—21no—
176C24×C59—21no—
177C24×C59—21no—
178C24×C59—21no—
179C24×C59—21no—
180C24×C59—21no—
181C24×C59—21no—
182C24×C59—21no—
183C24×C59C22×C412yes—
184C24×C59C22×C412yes—
185C24×C59C2×D412yes—
186C24×C59C2×D412yes—
187C24×C59C2×D412yes—
188C24×C59#4112yes—
189C24×C59C2411yescharacteristic
190C2×D4×C59—28no—
191C2×D4×C59—28no—
192C2×D4×C59—44no—
193C2×D4×C59—44no—
194C2×D4×C59—44no—
195C2×D4×C59—44no—
196C2×D4×C59—44no—
197C22×C4×C59—21no—
198C22×C4×C59—21no—
199C22×C4×C59—21no—
200C22×C4×C59—21no—
201C22×C4×C59—28no—
202C22×C4×C59—21no—
203C22×C4×C59—21no—
204C22×C4×C59—21no—
205C22×C4×C59—21no—
206C22×C4×C59—21no—
207C22×C4×C59—21no—
208C22×C4×C59—21no—
209C22×C4×C59—21no—
210C22×C4×C59—21no—
211C22×C4×C59—21no—
212C22×C4×C59—21no—
213C22×C4×C59—21no—
214C22×C4×C59—21no—
215C22×C4×C59—21no—
216C22×C4×C59—21no—
217C22×C4×C59—21no—
218C22×C4×C59—21no—
219C22×C4×C59—21no—
220C22×C4×C59—21no—
221C22×C4×C59—21no—
222C22×C4×C59—21no—
223C22×C4×C59—21no—
224C22×C4×C59—21no—
225C22×C4×C59—21no—
226C22×C4×C59—21no—
227C22×C4×C59—44no—
228C22×C4×C59—44no—
229C22×C4×C59—44no—
230C22×C4×C59—44no—
231C22×C4×C59—44no—
232C22×C4×C59—44no—
233C22×C4×C59C22×C412yes—
234C22×C4×C59C2×D412yes—
235C22×C4×C59C2×D412yes—
236C22×C4×C59#4112yes—
237C22×C4×C59#4112yes—
238C22×C4×C59#4112yes—
239C22×Dic59—21no—
240C22×Dic59—21no—
241C22×Dic59—21no—
242C22×Dic59—21no—
243C22×Dic59—21no—
244C22×Dic59—21no—
245C22×Dic59—21no—
246C22×Dic59—21no—
247C22×Dic59—28no—
248C22×Dic59—21no—
249C22×Dic59—21no—
250C22×Dic59—21no—
251C22×Dic59—21no—
252C22×Dic59—21no—
253C22×Dic59—21no—
254C22×Dic59—21no—
255C22×Dic59—21no—
256C22×Dic59—21no—
257C22×Dic59—21no—
258C22×Dic59—21no—
259C22×Dic59—21no—
260C22×Dic59—21no—
261C22×Dic59—21no—
262C22×Dic59—21no—
263C22×Dic59—21no—
264C22×Dic59—21no—
265C22×Dic59—21no—
266C22×Dic59—21no—
267C22×Dic59—21no—
268C22×Dic59—21no—
269C22×Dic59—21no—
270C22×Dic59—21no—
271C22×Dic59—21no—
272C22×Dic59—21no—
273C22×Dic59—21no—
274C22×Dic59—21no—
275C22×Dic59—21no—
276C22×Dic59—21no—
277C22×Dic59—21no—
278C22×Dic59—28no—
279C22×Dic59—21no—
280C22×Dic59—21no—
281C22×Dic59—21no—
282C22×Dic59—21no—
283C22×Dic59—21no—
284C22×Dic59—21no—
285C22×Dic59—21no—
286C22×Dic59—44no—
287C22×Dic59—44no—
288C22×Dic59—44no—
289C22×Dic59—44no—
290C22×Dic59—44no—
291C22×Dic59C22×C412yes—
292C22×Dic59C22×C412yes—
293C22×Dic59C22×C412yes—
294C22×Dic59C22×C412yes—
295C22×Dic59C2×D412yes—
296C22×Dic59C2×D412yes—
297C22×Dic59C2×D412yes—
298C22×Dic59C2×D412yes—
299C22×Dic59#4112yes—
300C22×Dic59#4112yes—
301C22×Dic59#4112yes—
302C22⋊C4×C59—28no—
303C22⋊C4×C59—44no—
304C22⋊C4×C59—44no—
305C22⋊Dic59—28no—
306C22⋊Dic59—28no—
307C22⋊Dic59—28no—
308C22⋊Dic59—28no—
309C22⋊Dic59—44no—
310C22⋊Dic59—44no—
311C22⋊Dic59C22⋊C4116yescomplemented
312Dic59⋊C4—28no—
313Dic59⋊C4—28no—
314Dic59⋊C4—44no—
315C4×Dic59—44no—
316C4×Dic59—44no—
317C4×Dic59—44no—
318C23×C59—22no—
319C23×C59—22no—
320C23×C59—22no—
321C23×C59—22no—
322C23×C59—22no—
323C23×C59—22no—
324C23×C59—22no—
325C23×C59—22no—
326C23×C59—22no—
327C23×C59—22no—
328C23×C59—22no—
329C23×C59—22no—
330C23×C59—22no—
331C23×C59—22no—
332C23×C59—22no—
333C23×C59—22no—
334C23×C59—22no—
335C23×C59—22no—
336C23×C59—22no—
337C23×C59—22no—
338C23×C59—22no—
339C23×C59—22no—
340C23×C59—22no—
341C23×C59—22no—
342C23×C59—22no—
343C23×C59—22no—
344C23×C59—22no—
345C23×C59—22no—
346C23×C59—22no—
347C23×C59—22no—
348C23×C59—22no—
349C23×C59—22no—
350C23×C59—22no—
351C23×C59—22no—
352C23×C59—22no—
353C23×C59—22no—
354C23×C59—41no—
355C23×C59—41no—
356C23×C59—41no—
357C23×C59—41no—
358C23×C59—41no—
359C23×C59—41no—
360C23×C59—41no—
361C23×C59—41no—
362C23×C59—41no—
363C23×C59—41no—
364C23×C59—41no—
365C23×C59—41no—
366C23×C59—41no—
367C23×C59—41no—
368C23×C59—41no—
369C23×C59—41no—
370C23×C59—41no—
371C23×C59—41no—
372C23×C59—41no—
373C23×C59—41no—
374C23×C59—41no—
375C23×C59—41no—
376C23×C59—41no—
377C23×C59—41no—
378C23×C59—41no—
379C23×C59—41no—
380C23×C59—41no—
381C23×C59—41no—
382C23×C59—41no—
383C23×C59—41no—
384C23×C59—41no—
385C23×C59—41no—
386C23×C59C2×C22⋊C414yes—
387C23×C59C4×D414yes—
388C23×C59C23×C411yescharacteristic
389C23×C59C22×D411yescharacteristic
390C23×C59C22×D411yescharacteristic
391C23×C59C22×D411yescharacteristic
392C23×C59C2×#4111yescharacteristic
393C23×C59C2×#4111yescharacteristic
394C23×C59C2×#4111yescharacteristic
395C23×C59C2×#4111yescharacteristic
396C23×C59C2×#4111yescharacteristic
397C23×C59C2×#4111yescharacteristic
398C23×C59C2×#4111yescharacteristic
399C23×C59H(5,𝔽2)11yescharacteristic
400C23×C59H(5,𝔽2)11yescharacteristic
401C23×C59H(5,𝔽2)11yescharacteristic
402C23×C592−1+411yescharacteristic
403D4×C59—416no—
404C2×C4×C59—22no—
405C2×C4×C59—22no—
406C2×C4×C59—22no—
407C2×C4×C59—22no—
408C2×C4×C59—22no—
409C2×C4×C59—22no—
410C2×C4×C59—22no—
411C2×C4×C59—22no—
412C2×C4×C59—22no—
413C2×C4×C59—22no—
414C2×C4×C59—22no—
415C2×C4×C59—22no—
416C2×C4×C59—22no—
417C2×C4×C59—22no—
418C2×C4×C59—22no—
419C2×C4×C59—416no—
420C2×C4×C59—41no—
421C2×C4×C59—41no—
422C2×C4×C59—41no—
423C2×C4×C59—41no—
424C2×C4×C59—41no—
425C2×C4×C59—41no—
426C2×C4×C59—41no—
427C2×C4×C59—41no—
428C2×C4×C59—41no—
429C2×C4×C59—41no—
430C2×C4×C59—41no—
431C2×C4×C59—41no—
432C2×C4×C59—41no—
433C2×C4×C59—41no—
434C2×C4×C59—41no—
435C2×C4×C59—41no—
436C2×C4×C59—41no—
437C2×C4×C59—41no—
438C2×C4×C59—41no—
439C2×C4×C59#12314yescomplemented
440C2×Dic59—22no—
441C2×Dic59—22no—
442C2×Dic59—22no—
443C2×Dic59—22no—
444C2×Dic59—22no—
445C2×Dic59—22no—
446C2×Dic59—22no—
447C2×Dic59—22no—
448C2×Dic59—22no—
449C2×Dic59—22no—
450C2×Dic59—22no—
451C2×Dic59—22no—
452C2×Dic59—22no—
453C2×Dic59—22no—
454C2×Dic59—22no—
455C2×Dic59—22no—
456C2×Dic59—22no—
457C2×Dic59—22no—
458C2×Dic59—22no—
459C2×Dic59—22no—
460C2×Dic59—22no—
461C2×Dic59—22no—
462C2×Dic59—22no—
463C2×Dic59—22no—
464C2×Dic59—22no—
465C2×Dic59—22no—
466C2×Dic59—22no—
467C2×Dic59—416no—
468C2×Dic59—41no—
469C2×Dic59—41no—
470C2×Dic59—41no—
471C2×Dic59—41no—
472C2×Dic59—41no—
473C2×Dic59—41no—
474C2×Dic59—41no—
475C2×Dic59—41no—
476C2×Dic59—41no—
477C2×Dic59—41no—
478C2×Dic59—41no—
479C2×Dic59—41no—
480C2×Dic59—41no—
481C2×Dic59—41no—
482C2×Dic59—41no—
483C2×Dic59—41no—
484C2×Dic59—41no—
485C2×Dic59—41no—
486C2×Dic59—41no—
487C2×Dic59—41no—
488C2×Dic59—41no—
489C2×Dic59—41no—
490C2×Dic59—41no—
491C2×Dic59—41no—
492C2×Dic59—41no—
493C2×Dic59—41no—
494C2×Dic59—41no—
495C2×Dic59C2×C22⋊C414yes—
496C2×Dic59C2×C22⋊C414yes—
497#14096—591nomaximal, Sylow
498C22×C59—24no—
499C22×C59—24no—
500C22×C59—24no—
501C22×C59—24no—
502C22×C59—24no—
503C22×C59—24no—
504C22×C59—42no—
505C22×C59—42no—
506C22×C59—42no—
507C22×C59—42no—
508C22×C59—42no—
509C22×C59—42no—
510C22×C59—42no—
511C22×C59—42no—
512C22×C59—42no—
513C22×C59—42no—
514C22×C59—42no—
515C22×C59—42no—
516C22×C59—42no—
517C22×C59—42no—
518C22×C59—42no—
519C22×C59—42no—
520C22×C59—42no—
521C22×C59—42no—
522C22×C59—42no—
523C22×C59—42no—
524C22×C59—42no—
525C22×C59—42no—
526C22×C59—42no—
527C22×C59—42no—
528C22×C59C22×C22⋊C411yescharacteristic
529C22×C59C2×C4×D411yescharacteristic
530C22×C59C4×#4111yescharacteristic
531C22×C59C4×#4111yescharacteristic
532C22×C59C4×#4111yescharacteristic
533C22×C59#51811yescharacteristic
534C22×C59#52011yescharacteristic
535C22×C59C2×#12311yescharacteristic
536C22×C59#52511yescharacteristic
537C22×C59#52511yescharacteristic
538C22×C59#52511yescharacteristic
539C22×C59#52911yescharacteristic
540C22×C59#52911yescharacteristic
541C22×C59#53211yescharacteristic
542C22×C59#53211yescharacteristic
543C22×C59#53811yescharacteristic
544C22×C59#53911yescharacteristic
545C22×C59#54011yescharacteristic
546C22×C59#54211yescharacteristic
547C22×C59D4211yescharacteristic
548C22×C59D4211yescharacteristic
549C22×C59#54611yescharacteristic
550C22×C59#54611yescharacteristic
551C22×C59#54611yescharacteristic
552C22×C59#54611yescharacteristic
553C22×C59#54611yescharacteristic
554C22×C59#54711yescharacteristic
555C22×C59#54711yescharacteristic
556C22×C59#54711yescharacteristic
557C22×C59#55111yescharacteristic
558C22×C59#55111yescharacteristic
559C22×C59#55211yescharacteristic
560C22×C59#55311yescharacteristic
561C22×C59#55311yescharacteristic
562C22×C59#55911yescharacteristic
563C4×C59—24no—
564C4×C59—42no—
565C4×C59—42no—
566C4×C59—42no—
567C4×C59—81no—
568Dic59—24no—
569Dic59—24no—
570Dic59—42no—
571Dic59—42no—
572Dic59—42no—
573Dic59—42no—
574Dic59—42no—
575Dic59—81no—
576C22×#123—591no—
577C2×#388—591no—
578C2×#386D5911yescharacteristic
579C2×C4×C22⋊C4—591no—
580C2×C4×C22⋊C4—591no—
581#1445—591no—
582#1440—591no—
583#1439—591no—
584#1438—591no—
585#1437—591no—
586#1436—591no—
587#1436—591no—
588C4⋊#95—591no—
589C22⋊#95—591no—
590C22⋊#95—591no—
591C2×C59—44no—
592C2×C59—44no—
593C2×C59#229711yescharacteristic
594C2×C59C4×#12311yescharacteristic
595C2×C59#233511yescharacteristic
596C2×C59D4×C22⋊C411yescharacteristic
597C2×C59#233911yescharacteristic
598C2×C59#235911yescharacteristic
599C2×C59#237411yescharacteristic
600C2×C59#241811yescharacteristic
601C2×C59#242211yescharacteristic
602C2×C59#245511yescharacteristic
603C2×C59#245711yescharacteristic
604C2×C59#246411yescharacteristic
605C2×C59#247011yescharacteristic
606C2×C59#255311yescharacteristic
607C2×C59#255711yescharacteristic
608C23×D4C2×D5911yescharacteristic
609C24×C4—591no—
610C24×C4C2×D5911yescharacteristic
611C2×#123—598no—
612C2×#123—1184no—
613C2×#123—1184no—
614C22×C4⋊C4—591no—
615C22×C4⋊C4—591no—
616C22×C4⋊C4—591no—
617C22×C22⋊C4—591no—
618C22×C22⋊C4—591no—
619C22×C22⋊C4—591no—
620C22×C22⋊C4—591no—
621C22×C22⋊C4—591no—
622C22×C22⋊C4—591no—
623C22×C22⋊C4—591no—
624C22×C22⋊C4C2×D5911yescharacteristic
625C22×C22⋊C4C2×D5911yescharacteristic
626C22×C22⋊C4C2×D5911yescharacteristic
627C22×C42—591no—
628C22×C42—591no—
629C22×C42—591no—
630#388—1184no—
631#386—24no—
632C4×C22⋊C4—1184no—
633C4×C22⋊C4—1184no—
634C2×#95—591no—
635C2×#95—591no—
636C2×#95—591no—
637C2×#95—591no—
638C2×#95—591no—
639C2×#95—591no—
640C2×#95—591no—
641C2×#95—591no—
642C2×#95—591no—
643C2×#95—591no—
644C2×#95—591no—
645C2×#95—591no—
646C2×#95—591no—
647C2×#95—591no—
648C2×#95C2×D5911yescharacteristic
649C2×#95C2×D5911yescharacteristic
650C59#1409611yescharacteristic, complemented, Sylow
651C25C22×D5911yescharacteristic
652C25C22×D5911yescharacteristic
653C22×D4—22no—
654C22×D4—22no—
655C22×D4—22no—
656C22×D4—22no—
657C22×D4—41no—
658C22×D4—41no—
659C22×D4C4×D5914yes—
660C23×C4—22no—
661C23×C4—22no—
662C23×C4—22no—
663C23×C4—22no—
664C23×C4—22no—
665C23×C4—41no—
666C23×C4—41no—
667C23×C4—591no—
668C23×C4—591no—
669C23×C4—591no—
670C23×C4—591no—
671C23×C4—591no—
672C23×C4—591no—
673C23×C4—591no—
674C23×C4—594no—
675C23×C4—591no—
676C23×C4—1182no—
677C23×C4—1182no—
678C23×C4—1182no—
679C23×C4—1182no—
680C23×C4—2361no—
681C23×C4—2361no—
682C23×C4C22×D5911yescharacteristic
683C23×C4C22×D5911yescharacteristic
684C23×C4C22×D5911yescharacteristic
685C23×C4C22×D5911yescharacteristic
686C23×C4C22×D5911yescharacteristic
687#123—11832no—
688C2×C4⋊C4—594no—
689C2×C4⋊C4—594no—
690C2×C4⋊C4—1182no—
691C2×C4⋊C4—1182no—
692C2×C4⋊C4—1182no—
693C2×C4⋊C4—1182no—
694C2×C4⋊C4—1182no—
695C2×C4⋊C4—1182no—
696C2×C4⋊C4—2361no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—41no—
704C2×C22⋊C4—41no—
705C2×C22⋊C4—594no—
706C2×C22⋊C4—594no—
707C2×C22⋊C4—594no—
708C2×C22⋊C4—594no—
709C2×C22⋊C4—594no—
710C2×C22⋊C4—1182no—
711C2×C22⋊C4—1182no—
712C2×C22⋊C4—1182no—
713C2×C22⋊C4—1182no—
714C2×C22⋊C4—1182no—
715C2×C22⋊C4—1182no—
716C2×C22⋊C4—1182no—
717C2×C22⋊C4—1182no—
718C2×C22⋊C4—1182no—
719C2×C22⋊C4—1182no—
720C2×C22⋊C4—1182no—
721C2×C22⋊C4—1182no—
722C2×C22⋊C4—1182no—
723C2×C22⋊C4—1182no—
724C2×C22⋊C4—2361no—
725C2×C22⋊C4—2361no—
726C2×C22⋊C4C22⋊D5914yes—
727C2×C42—1182no—
728C2×C42—1182no—
729C2×C42—1182no—
730C2×C42—1182no—
731C2×C42—1182no—
732C2×C42—1182no—
733C2×C42—2361no—
734C2×C42—2361no—
735C2×C42—2361no—
736#95—22no—
737#95—22no—
738#95—1182no—
739#95—1182no—
740#95—1182no—
741#95—1182no—
742#95—1182no—
743#95—1182no—
744#95—1182no—
745#95—1182no—
746#95—1182no—
747#95—1182no—
748#95—2361no—
749#95—2361no—
750#95—2361no—
751#95—2361no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24C2×C4×D5912yes—
777C24C2×C4×D5912yes—
778C24#1174568512yes—
779C24D4×D5912yes—
780C24D4×D5912yes—
781C24C2×C22⋊D5912yes—
782C24C23×D5911yescharacteristic
783C2×D4—28no—
784C2×D4—28no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—44no—
788C2×D4—44no—
789C2×D4—44no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—28no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—44no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—592no—
827C22×C4—592no—
828C22×C4—592no—
829C22×C4—592no—
830C22×C4—592no—
831C22×C4—592no—
832C22×C4—592no—
833C22×C4—592no—
834C22×C4—592no—
835C22×C4—592no—
836C22×C4—592no—
837C22×C4—1188no—
838C22×C4—1181no—
839C22×C4—1181no—
840C22×C4—1181no—
841C22×C4—1181no—
842C22×C4—1181no—
843C22×C4—1181no—
844C22×C4—1181no—
845C22×C4—1181no—
846C22×C4—1188no—
847C22×C4—1181no—
848C22×C4—1181no—
849C22×C4—1181no—
850C22×C4—1181no—
851C22×C4—1181no—
852C22×C4—1181no—
853C22×C4—1181no—
854C22×C4—1181no—
855C22×C4—1181no—
856C22×C4—1181no—
857C22×C4—1181no—
858C22×C4—1181no—
859C22×C4—1181no—
860C22×C4—1181no—
861C22×C4—1181no—
862C22×C4—1181no—
863C22×C4—1181no—
864C22×C4—1181no—
865C22×C4—1181no—
866C22×C4—1181no—
867C22×C4—1181no—
868C22×C4—1181no—
869C22×C4—1181no—
870C22×C4—1181no—
871C22×C4—1181no—
872C22×C4—1181no—
873C22×C4—1181no—
874C22×C4—1181no—
875C22×C4—1181no—
876C22×C4—1181no—
877C22×C4—1181no—
878C22×C4—1181no—
879C22×C4—1181no—
880C22×C4—1181no—
881C22×C4—1181no—
882C22×C4—1181no—
883C22×C4—1181no—
884C22×C4—2364no—
885C22×C4—2364no—
886C22×C4—2364no—
887C22×C4—2364no—
888C22×C4—2364no—
889C22×C4C2×C4×D5912yes—
890C22×C4#1174568712yes—
891C22×C4#1174568712yes—
892C22×C4#1174568712yes—
893C22×C4C2×C22⋊D5912yes—
894C22×C4C2×C22⋊D5912yes—
895C4⋊C4—1188no—
896C4⋊C4—1188no—
897C4⋊C4—2364no—
898C22⋊C4—28no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C22⋊C4—5916no—
902C22⋊C4—1188no—
903C22⋊C4—1188no—
904C22⋊C4—1188no—
905C22⋊C4—1188no—
906C22⋊C4—2364no—
907C22⋊C4—2364no—
908C42—2364no—
909C42—2364no—
910C42—2364no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23C22⋊C4×D5914yes—
980C23C4×C22⋊D5914yes—
981C23C22×C4×D5911yescharacteristic
982C23C2×D4×D5911yescharacteristic
983C23C2×D4×D5911yescharacteristic
984C23C22×C22⋊D5911yescharacteristic
985C23#41×D5911yescharacteristic
986C23#41×D5911yescharacteristic
987C23#41×D5911yescharacteristic
988C23C2×#1174568711yescharacteristic
989C23C2×#1174568711yescharacteristic
990C23C2×#1174568711yescharacteristic
991C23C2×#1174568511yescharacteristic
992C23#1427377211yescharacteristic
993C23#1427377211yescharacteristic
994C23#1427377211yescharacteristic
995C23#1427377411yescharacteristic
996D4—416no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—416no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—594no—
1033C2×C4—594no—
1034C2×C4—1182no—
1035C2×C4—1182no—
1036C2×C4—1182no—
1037C2×C4—1182no—
1038C2×C4—1182no—
1039C2×C4—1182no—
1040C2×C4—1182no—
1041C2×C4—1182no—
1042C2×C4—1182no—
1043C2×C4—1182no—
1044C2×C4—1182no—
1045C2×C4—1182no—
1046C2×C4—1182no—
1047C2×C4—1182no—
1048C2×C4—1182no—
1049C2×C4—1182no—
1050C2×C4—1182no—
1051C2×C4—1182no—
1052C2×C4—1182no—
1053C2×C4—1182no—
1054C2×C4—1182no—
1055C2×C4—1182no—
1056C2×C4—1182no—
1057C2×C4—1182no—
1058C2×C4—1182no—
1059C2×C4—1182no—
1060C2×C4—1182no—
1061C2×C4—23616no—
1062C2×C4—2361no—
1063C2×C4—2361no—
1064C2×C4—2361no—
1065C2×C4—2361no—
1066C2×C4—2361no—
1067C2×C4—2361no—
1068C2×C4—2361no—
1069C2×C4—2361no—
1070C2×C4—2361no—
1071C2×C4—2361no—
1072C2×C4—2361no—
1073C2×C4—2361no—
1074C2×C4—2361no—
1075C2×C4—2361no—
1076C2×C4—2361no—
1077C2×C4—2361no—
1078C2×C4—2361no—
1079C2×C4—2361no—
1080C2×C4—2361no—
1081C2×C4—2361no—
1082C2×C4—2361no—
1083C2×C4—2361no—
1084C2×C4—2361no—
1085C2×C4—2361no—
1086C2×C4—2361no—
1087C2×C4—2361no—
1088C2×C4—2361no—
1089C2×C4#1427370814yescomplemented
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—24no—
1094C22—24no—
1095C22—24no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22C2×C22⋊C4×D5911yescharacteristic
1121C22C2×C4×C22⋊D5911yescharacteristic
1122C22C4×#1174568711yescharacteristic
1123C22C4×#1174568711yescharacteristic
1124C22C4×#1174568711yescharacteristic
1125C22#1683787511yescharacteristic
1126C22#1683788111yescharacteristic
1127C22C2×#1427370811yescharacteristic
1128C22#1683790811yescharacteristic
1129C22#1683790911yescharacteristic
1130C22#1683791011yescharacteristic
1131C22#1683793211yescharacteristic
1132C22#1683793211yescharacteristic
1133C22#1683794711yescharacteristic
1134C22#1683794711yescharacteristic
1135C22#1683798711yescharacteristic
1136C22#1683799511yescharacteristic
1137C22#1683800211yescharacteristic
1138C22#1683801911yescharacteristic
1139C22D4×C22⋊D5911yescharacteristic
1140C22D4×C22⋊D5911yescharacteristic
1141C22#1683803911yescharacteristic
1142C22#1683804111yescharacteristic
1143C22#1683804211yescharacteristic
1144C22#1683804211yescharacteristic
1145C22#1683804611yescharacteristic
1146C22#1683805011yescharacteristic
1147C22#1683805111yescharacteristic
1148C22#1683805211yescharacteristic
1149C22#1683808111yescharacteristic
1150C22#1683808311yescharacteristic
1151C22#1683809211yescharacteristic
1152C22#1683809911yescharacteristic
1153C22#1683809911yescharacteristic
1154C22#1683813611yescharacteristic
1155C4—24no—
1156C4—42no—
1157C4—42no—
1158C4—42no—
1159C4—81no—
1160C4—1184no—
1161C4—1184no—
1162C4—4721no—
1163C4—2362no—
1164C4—2362no—
1165C4—2362no—
1166C4—2362no—
1167C4—2362no—
1168C2—44no—
1169C2—44no—
1170C2#2142658111yescharacteristic
1171C2C4×#1427370811yescharacteristic
1172C2#2142688711yescharacteristic
1173C2C22⋊C4×C22⋊D5911yescharacteristic
1174C2#2142692211yescharacteristic
1175C2#2142708211yescharacteristic
1176C2#2142722911yescharacteristic
1177C2#2142755411yescharacteristic
1178C2#2142760611yescharacteristic
1179C2#2142797511yescharacteristic
1180C2#2142800011yescharacteristic
1181C2#2142809811yescharacteristic
1182C2#2142818911yescharacteristic
1183C2#2142913811yescharacteristic
1184C2#2142919211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC2×C59×#386C2
socle, cosocleC24×C59C24
prime radicalC23×D4×C59C22
hypercenterC2×#386D59
hypocenterC59#14096
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#386

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#16837290C2semidirect
3. C2×C22⋊C4×Dic59C2semidirect
4. C2×C4×C22⋊Dic59C2semidirect
5. #21422362C2semidirect
6. #21422343C2semidirect
7. #21422339C2semidirect
9. #21422333C2semidirect
10. #21422327C2semidirect
11. #21422327C2semidirect
12. Dic59⋊#95C2semidirect
13. #21422319C2semidirect
14. #21422318C2semidirect
19. C2×#14273708C4semidirect
64. C23×Dic59C2×C4semidirect
81. C2×Dic59⋊C4C2×C4semidirect
82. C2×Dic59⋊C4C2×C4semidirect
101. C2×C22⋊Dic59C2×C4semidirect
311. C22⋊Dic59C22⋊C4semidirect
439. C2×C4×C59#123semidirect
650. C59#14096semidirect
1089. C2×C4#14273708semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#142737082
C2×#168372902
C2×C22⋊C4×Dic592
C2×C4×C22⋊Dic592
#214223622
#214223432
#214223392
#214223372
#214223332
#214223272
Dic59⋊#952
#214223192
#214223182
C2×C59×#3862
#1409659